We consider a SU(2) lattice gauge theory on the square lattice, with a single fundamental complex fermion and a single fundamental complex boson on each lattice site. Projective symmetries of the gaugecharged fermions are chosen so that they match with those of the spinons of the$\pi $flux spin liquid. Global symmetries of all gaugeinvariant observables are chosen to match with those of the particlehole symmetric electronic Hubbard model at halffilling. Consequently, both the fundamental fermion and fundamental boson move in an average background$\pi $flux, their gaugeinvariant composite is the physical electron, and eliminating gauge fields in a strong gaugecoupling expansion yields an effective extended Hubbard model for the electrons. The SU(2) gauge theory displays several confining/Higgs phases: a nodal$d$wave superconductor, and states with Néel, valencebond solid, charge, or staggered current orders. There are also a number of quantum phase transitions between these phases that are very likely described by$(2+1)$dimensional deconfined conformal gauge theories, and we present large flavor expansions for such theories. These include the phenomenologically attractive case of a transition between a conventional insulator with a charge gap and Néel order, and a conventional$d$wave superconductor with gapless Bogoliubov quasiparticles at four nodal points in the Brillouin zone. We also apply our approach to the honeycomb lattice, where we find a bicritical point at the junction of Néel, valence bond solid (Kekulé), and Dirac semimetal phases.
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Published by the American Physical Society 2024 Free, publiclyaccessible full text available July 1, 2025 
Abstract We model the pseudogap state of the hole and electrondoped cuprates as a metal with hole and/or electron pocket Fermi surfaces. In the absence of longrange antiferromagnetism, such Fermi surfaces violate the Luttinger requirement of enclosing the same area as free electrons at the same density. Using the Ancilla theory of such a pseudogap state, we describe the onset of conventional
d wave superconductivity by the condensation of a chargee Higgs boson transforming as a fundamental under the emergent SU(2) gauge symmetry of a backgroundπ flux spin liquid. In all cases, we find that thed wave superconductor has gapless Bogoliubov quasiparticles at 4 nodal points on the Brillouin zone diagonals with significant velocity anisotropy, just as in the BCS state. This includes the case of the electrondoped pseudogap metal with only electron pockets centered at wavevectors (π , 0), (0,π ), and an electronic gap along the zone diagonals. Remarkably, in this case, too, gapless nodal Bogoliubov quasiparticles emerge within the gap at 4 points along the zone diagonals upon the onset of superconductivity. 
Abstract The superconducting state and mechanism are among the least understood phenomena in twisted graphene systems. Recent tunneling experiments indicate a transition between nodal and gapped pairing with electron filling, which is not naturally understood within current theory. We demonstrate that the coexistence of superconductivity and flavor polarization leads to pairing channels that are guaranteed by symmetry to be entirely bandoffdiagonal, with a variety of consequences: most notably, the pairing invariant under all symmetries can have Bogoliubov Fermi surfaces in the superconducting state with protected nodal lines, or may be fully gapped, depending on parameters, and the bandoffdiagonal chiral
p wave state exhibits transitions between gapped and nodal regions upon varying the doping. We demonstrate that bandoffdiagonal pairing can be the leading state when only phonons are considered, and is also uniquely favored by fluctuations of a timereversalsymmetric intervalley coherent order motivated by recent experiments. Consequently, bandoffdiagonal superconductivity allows for the reconciliation of several key experimental observations in graphene moiré systems.Free, publiclyaccessible full text available December 1, 2024 
We describe the confining instabilities of a proposed quantum spin liquid underlying the pseudogap metal state of the holedoped cuprates. The spin liquid can be described by a SU(2) gauge theory of
N _{f}= 2 massless Dirac fermions carrying fundamental gauge charges—this is the lowenergy theory of a meanfield state of fermionic spinons moving on the square lattice withπ flux per plaquette in the ℤ_{2}center of SU(2). This theory has an emergent SO(5)_{f}global symmetry and is presumed to confine at low energies to the Néel state. At nonzero doping (or smaller Hubbard repulsionU at halffilling), we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges also moving inπ ℤ_{2}flux. At halffilling, the lowenergy theory of the Higgs sector hasN _{b}= 2 relativistic bosons with a possible emergent SO(5)_{b}global symmetry describing rotations between ad wave superconductor, period2 charge stripes, and the timereversal breaking “d density wave” state. We propose a conformal SU(2) gauge theory withN _{f}= 2 fundamental fermions,N _{b}= 2 fundamental bosons, and a SO(5)_{f}×SO(5)_{b}global symmetry, which describes a deconfined quantum critical point between a confining state which breaks SO(5)_{f}and a confining state which breaks SO(5)_{b}. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order andd wave superconductivity. A similar theory applies at nonzero doping and largeU , with longerrange couplings of the chargons leading to charge order with longer periods. 
We investigate a model of electrons with random and alltoall hopping and spin exchange interactions, with a constraint of no double occupancy. The model is studied in a Sachdev–Ye–Kitaevlike large
M limit with SU(M ) spin symmetry. The saddlepoint equations of this model are similar to approximate dynamic meanfield equations of realistic, nonrandom,t J models. We use numerical studies on both real and imaginary frequency axes, along with asymptotic analyses, to establish the existence of a critical non–Fermiliquid metallic ground state at large doping, with the spin correlation exponent varying with doping. This critical solution possesses a timereparameterization symmetry, akin to Sachdev–Ye–Kitaev (SYK) models, which contributes a linearintemperature resistivity over the full range of doping where the solution is present. It is therefore an attractive meanfield description of the overdoped region of cuprates, where experiments have observed a linearT resistivity in a broad region. The critical metal also displays a strong particle–hole asymmetry, which is relevant to Seebeck coefficient measurements. We show that the critical metal has an instability to a lowdoping spinglass phase and compute a critical doping value. We also describe the properties of this metallic spinglass phase. 
Recent experiments on twisted bilayer graphene have shown a hightemperature parent state with massless Dirac fermions and broken electronic flavor symmetry; superconductivity and correlated insulators emerge from this parent state at lower temperatures. We propose that the superconducting and correlated insulating orders are connected by Wess–Zumino–Witten terms, so that defects of one order contain quanta of another order and skyrmion fluctuations of the correlated insulator are a “mechanism” for superconductivity. We present a comprehensive listing of plausible lowtemperature orders and the parent flavor symmetrybreaking orders. The previously characterized topological nature of the band structure of twisted bilayer graphene plays an important role in this analysis.